A241851 - OEIS

%I #18 Nov 29 2024 19:08:13

%S 21,22,25,30,37,46,57,70,85,102,121,142,165,190,217,246,277,310,345,

%T 382,421,462,505,550,597,646,697,750,805,862,921,982,1045,1110,1177,

%U 1246,1317,1390,1465,1542,1621,1702,1785,1870,1957,2046,2137,2230,2325,2422,2521

%N a(n) = n^2 + 21.

%H Vincenzo Librandi, <a href="/A241851/b241851.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: (21 - 41*x + 22*x^2)/(1 - x)^3.

%F a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.

%F From _Amiram Eldar_, Nov 04 2020: (Start)

%F Sum_{n>=0} 1/a(n) = (1 + sqrt(21)*Pi*coth(sqrt(21)*Pi))/42.

%F Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(21)*Pi*cosech(sqrt(21)*Pi))/42. (End)

%F E.g.f.: exp(x)*(21 + x + x^2). - _Elmo R. Oliveira_, Nov 29 2024

%t Table[n^2 + 21, {n, 0, 60}]

%o (Magma) [n^2+21: n in [0..60]];

%o (PARI) a(n)=n^2+21 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. similar sequence listed in A114962.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, May 01 2014